Fluctuation dissipation ratio in the one dimensional kinetic Ising model

The exact relation between the response function $R(t,t^{\mathrm{\prime }})$ and the two time correlation function $C(t,t^{\mathrm{\prime }})$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\mathrm{\prime }})$ is found to depend on time through $C(t,t^{\mathrm{\prime }})$ in the time region where scaling $C(t,t^{\prime}) = f(t/t^{\prime})$holds\mathrm{.}Thecrossoverfromthenontrivialform$X(C(t,t^{\prime}))$to$X(t,t^{\prime}) \equiv 1$ takes place as the waiting time $t_w$ is increased from below to above the equilibration time $t_{eq}$.